Recurrence
摘要
Chapter 3 is concerned with recurrence of switching diffusion processes. Enabling the Markov process returns to any compact set infinitely often with probability one, recurrence guarantees long-term stability by preventing the process from escaping to infinity and ensures the existence of an invariant measure under appropriate conditions. This chapter provides a systematic study on the recurrence of switching diffusion processes. It establishes sufficient conditions for recurrence, transience, positive recurrence, and null recurrence using appropriate Lyapunov functions. Furthermore, it provides easily verifiable conditions for positive recurrence of linearized systems.